(CNN) -- Amnesty International has joined the ranks of those criticizing the U.S. Border Patrol, calling for a "full, impartial and transparent investigation" into a shooting this week that left a 15-year-old Mexican boy dead.

"This shooting across the border appears to have been a grossly disproportionate response and flies in the face of international standards which compel police to use firearms only as a last resort, in response to an immediate, deadly threat that cannot be contained through lesser means," said Susan Lee, Americas director at Amnesty International, in a statement Wednesday on the organization's website.

The Mexican government also has requested a quick and public investigation into the fatal shooting at the border between El Paso, Texas, and Ciudad Juarez, Mexico, on Monday night. The teen was shot during a rock-throwing incident, Mexican and U.S. officials said.

On Wednesday, State Department spokesman P.J. Crowley said the United States will ensure a thorough investigation.

"We pledge that (the) investigation will be fully transparent," he said.

"We understand the concern that they have about not just this incident, but multiple incidents where we've had tragic loss of life at the border," Crowley added.

A long-term solution to avoid these kind of incidents would be the passage of comprehensive immigration reform, he said.

Border Patrol agents responded to a call of a possible immigrant smuggling taking place on the border, the FBI said. The agents were able to apprehend two suspects while others crossed back into Mexico and threw rocks at an agent, who then fired shots.

Sergio Adrian Hernandez Huereca was killed by a shot to the head, officials said.

It was unclear whether Hernandez was on the U.S. or Mexican side of the border when he was shot, though his body was found on the Mexican side, the FBI said.

There were videocameras in the area that the FBI is reviewing, El Paso FBI spokeswoman Andrea Simmons said.

Simmons said the FBI will decline further comment until the investigation is complete. The agency's version of events is based not just on the Border Patrol's statements but on interviews with civilians and other evidence, Simmons said.

"I don't want it to seem like it was one-sided information," she said.

The border patrol agent "was a coward. He shouldn't have done that because my son was in Mexico, not the United States," Hernandez's mother, Maria Guadalupe Huereca, told CNN en Espaņol on Wednesday.

The boy was not going to cross into the United States, she said.

Instead, he had gone to visit his brother, who works for the Mexican customs agency, to pick up some money so he could by school supplies, Huereca said. After picking up the money, the boy went near the international bridge, where he hid behind a pillar when the shots rang out, she said.

"If (the border patrol agent) has children, he will see my child's face when he killed him," Huereca said. "May God forgive him for what he did to my son."

The shooting comes less than two weeks after the May 31 death of a Mexican illegal immigrant who had been detained three days earlier by border agents in California.

San Diego police, who are investigating the death of Anastasio Hernandez, said he was beaten with a baton and shot with a stun gun after he became combative. California medical officials ruled his death a homicide.